Complex lens for a tandem scanning optical system and a manufacturing method thereof

ABSTRACT

A complex lens for a tandem scanning optical system converges a plurality of light beams, which are modulated independently and deflected by a deflector, onto a surface to be scanned, and forms a plurality of scanning lines at the same time. The complex lens includes a plurality of stacked lens portions that are molded as a single-piece element. Thus a plurality of lens surfaces of the lens portions at an incident side are formed by a single-piece mirror surface core and a plurality of lens surfaces of the lens portions at an exit side are formed by another single-piece mirror surface core during the molding process.

This application is a divisional of U.S. patent application Ser. No.09/987,871, filed Nov. 16, 2001 now U.S. Pat. No. 6,790,389, thedisclosure of which is expressly incorporated herein by reference in itsentirety.

BACKGROUND OF THE INVENTION

The present invention relates to a complex lens that consists of aplurality of stacked lens portions, and particularly, relates to thecomplex lens for a tandem scanning optical system employed in an imagingdevice such as a color laser printer for converging a plurality of lightbeams deflected by a deflector. Further, the present invention relatesto a manufacturing method of such a complex lens for a tandem scanningoptical system.

A tandem scanning optical system employed in a color laser printer isprovided with four semiconductor lasers and four photoconductive drumsthat correspond to colors Y (Yellow), M (Magenta), C (Cyan) and K(blacK), respectively. In such a tandem scanning optical system, it ispreferable to make at least one part of the optical system shareableamong the colors to downsize the system. The polygon mirror may beshared.

When a polygon mirror is shared, four light beams are incident on thepolygon mirror such that they are arranged in an auxiliary scanningdirection, which is coincident with a direction of the rotation axis ofthe polygon mirror. The four light beams deflected by the polygon mirrorare converged by an fθ lens and the optical paths thereof are separatedby mirrors. The separated four light beams form scanning lines on therespective photoconductive drums.

It is preferable that the four light beams deflected by the polygonmirror are converged by the respective lens elements in order to obtainthe most suitable optical performance. On the other hand, the smallerthe thickness of the polygon mirror is, the smaller the spaces among thefour light beams are in the vicinity of the polygon mirror. This doesnot allow employing independent lens elements for the respective lightbeams. Therefore, a lens in the fθ e lens arranged close to the polygonmirror should be a complex lens that consists of stacked four lensportions.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to provide an improvedmanufacturing method of a complex lens for a tandem scanning opticalsystem that is capable of reducing the positional error among the lensportions when the complex lens that consists of stacked lens portions ismolded as a single-piece element.

For the above object, according to the present invention, there isprovided a manufacturing method of a complex lens for a tandem scanningoptical system, including a step for preparing molding dies for forminga cavity to form the complex lens as a single-piece element, and a stepfor injecting lens material into the cavity. The molding dies include apair of single-piece mirror surface cores that form a plurality of lenssurfaces of the complex lens at an incident side and a plurality of lenssurfaces at an exit side, respectively. The complex lens consists of aplurality of stacked lens portions for converging a plurality of lightbeams, which are modulated independently and deflected by a deflector,onto a surface to be scanned, respectively, for forming a plurality ofscanning lines at the same time.

Further, a complex lens for a tandem scanning optical system accordingto the present invention is formed as a single-piece element that isequivalent to a combination of independent lens portions stacked one onanother, the lens surfaces of the lens portions at the incident side areformed by a single-piece mirror surface core and the lens surface of thelens portions at the exit side are formed by another single-piece mirrorsurface core.

Since the lens surfaces at the incident side and the lens surface at theexit side are formed by the single-piece mirror surface cores,respectively, during the molding process, the relative positional erroramong the lens surfaces at the incident side and that at the exit sidecan be reduced.

It is preferable that each of the mirror surface portions of the mirrorsurface cores has a concave sectional shape in a direction perpendicularto the direction in which a plurality of light beams scan (i.e., anauxiliary scanning direction). That is, the lens surfaces of the moldedcomplex lens preferably have convex sectional shapes in the directionperpendicular to the scanning direction of the light beam.

When the mirror surface portions of the mirror surface core have convexsectional shapes, the boundary of the mirror surface portions will be avalley. Therefore, the boundary portions cannot be sharply processedbecause of the limitation of a cutting tool, which requirespredetermined margins at the boundaries. The margins are not employed aslens surfaces.

On the other hand, when the mirror surface portions of the mirrorsurface core have concave sectional shapes, the boundary of the mirrorsurface portions will be a peak. Therefore, since the boundary portionscan be sharply processed by the cutting tool, the mirror surfaceportions can be processed without the margins.

The mirror surface portions of at least one of the mirror surface coresat the incident and exit sides may be formed as rotationally-symmetricalconcave surfaces with respect to respective optical axes such asspherical surfaces. In such a case, the lens surfaces of at least one ofthe incident and exit sides are formed as rotationally-symmetricalconvex surfaces with respect to respective optical axes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a sectional view of a cavity and surroundings of an injectionmolding machine to mold a complex lens for a tandem scanning opticalsystem according to embodiments;

FIG. 1B is a sectional view of the complex lens molded by the injectionmolding machine of FIG. 1A;

FIG. 2 is a perspective view of a mirror surface core employed in theinjection molding machine of FIG. 1A;

FIG. 3 is a sectional view of the injection molding machine to mold thecomplex lens of the embodiments;

FIG. 4 shows a tandem scanning optical system that employs the complexlens of FIG. 1B in the auxiliary scanning direction;

FIG. 5 shows a scanning optical system of a first embodiment in the mainscanning direction;

FIG. 6 shows the scanning optical system of the first embodiment in theauxiliary scanning direction;

FIG. 7A is a graph showing a linearity error of the scanning opticalsystem of the first embodiment;

FIG. 7B is a graph showing a curvature of field of the scanning opticalsystem of the first embodiment;

FIG. 8 shows a scanning optical system of a second embodiment in themain scanning direction;

FIG. 9 shows the scanning optical system of the second embodiment in theauxiliary scanning direction;

FIG. 10A is a graph showing a linearity error of the scanning opticalsystem of the second embodiment; and

FIG. 10B is a graph showing a curvature of field of the scanning opticalsystem of the second embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A method for manufacturing a complex lens for a tandem scanning opticalsystem will be described with reference to FIGS. 1 through 3. FIG. 1A isa sectional view of a cavity and surroundings of an injection moldingmachine to mold the complex lens according to embodiments; FIG. 1B is asectional view of the molded complex lens; FIG. 2 is a perspective viewof a mirror surface core; and FIG. 3 is a sectional view of theinjection molding machine.

The complex lens is formed as a single-piece element through aninjection molding process. Molding dies used in the process includecores having mirror-finished surfaces to form incident lens surfaces andexit lens surfaces of the lens portions. The core is called a “mirrorsurface core” in this specification.

The general construction of the injection molding machine will bedescribed with reference to FIG. 3. The machine is provided with firstand second retainer plates 2 and 3 that can slide in a right-leftdirection in the drawing in cylinders 1 a and 1 b located at right andleft sides. The retainer plates 2 and 3 have hollows at the facesopposed to each other and mirror surface cores 4 and 5 are installed inthe hollows, respectively. A cavity 6 is formed as a space surrounded bymolding dies, which include the first and second retainer plates 2, 3,and the mirror surface cores 4 and 5, when the retainer plates 2 and 3close to contact with each other. Further, the first and second retainerplates 2 and 3 are connected with driving rods 7 and 8, respectively,and the movement of the rods 7 and 8 in the right-left direction drivesthe retainer plates 2 and 3 to close them up and to move them away.

During the molding process, as shown in FIG. 3, the first and secondretainer plates 2 and 3 get closer to contact with each other and moltenresin is injected into the cavity 6 through a runner (not shown). Afterthe predetermined cooling time is elapsed from the injection, theretainer plates 2 and 3 are moved away and the molded complex lens isretrieved from the molding dies.

The molded complex lens 20 is formed as a single-piece element that isequivalent to a combination of independent four lens portions stackedone on another, as shown in FIG. 1B. The complex lens 20 has fourincident lens surfaces 21 and four exit lens surfaces 22. In FIG. 1B, anx-direction is a direction parallel to each of optical axes of the lensportions, a y-direction is a direction along which the light beams aredeflected by a polygon mirror (referred to as a main scanningdirection), and a z-direction is a direction perpendicular to the x- andy-directions (referred to as an auxiliary scanning direction). Theincident lens surfaces 21 and the exit lens surfaces 22 have convexsectional shapes in the auxiliary scanning direction. Further, in FIG.1B, the convex shapes of the lens surfaces are exaggerated for purposesof illustration.

The incident lens surfaces 21 are formed (i.e., molded) by thesingle-piece mirror surface core 4 and the exit lens surfaces 22 areformed (i.e., molded) by the single-piece mirror surface core 5. Asshown in FIG. 1A and FIG. 2, the mirror surface core 4 is formed as asingle-piece element and is provided with four mirror surface portions 4a that are formed independently to form four lens surfaces. The mirrorsurface portions 4 a have concave sectional shapes in both of the mainand auxiliary scanning directions. The other mirror surface core 5 isformed as a single-piece element and is provided with four mirrorsurface portions 5 a that have concave sectional shapes in at least theauxiliary scanning direction.

If the mirror surface cores are independent of one another (i.e., onecore corresponds to one lens surface), there may be relative positionalerrors among the respective mirror surface cores. Since the positionalerror of the cores results in the positional error among the lenssurfaces of the molded complex lens, the image forming performancedeteriorates.

On the other hand, since the incident lens surfaces 21 and the exit lenssurfaces 22 are formed by the single-piece mirror surface cores 4 and 5,respectively, during the molding process, the relative positional erroramong the incident lens surfaces 21 and the relative positional erroramong the exit lens surfaces 22 can be reduced. Further, since themirror surface portions 4 a and 5 a have concave sectional shapes in theauxiliary scanning direction, each of the boundaries of the mirrorsurface portions 4 a and 5 a are formed as a peak that can be sharplyprocessed by the cutting tool. Therefore, the mirror surface portionscan be processed without the margins at the boundary portions, whichavoids upsizing of the lens surfaces 21 and 22 in the auxiliary scanningdirection more than necessary.

FIG. 4 is a general description of a tandem scanning optical system,which employs the complex lens manufactured by the above-describedmethod, in the auxiliary scanning direction.

The tandem scanning optical system deflects the four laser beams, whichare emitted from light source portion (not shown) and modulatedindependently, by means of a polygon mirror 30 at the same time, andconverges the four laser beams onto the respective photoconductive drums41, 42, 43 and 44. Rotation of the polygon mirror 30 about a rotationaxis 30 a scans the laser beam on the photoconductive drums to form fourscanning lines at the same time.

An fθ lens to converge the light beams consists of a first lens 51 and asecond lens 52 that are located in the vicinity of the polygon mirror30, and third lenses 53 a, 53 b, 53 c and 53 d that are located on therespective optical paths divided by mirrors 71 to 78. The first andsecond lenses 51 and 52 are the complex lenses, each of which is formedas a single-piece element and it is equivalent to the combination offour independent lens portions stacked one on another as shown in FIG.1B. Further, each of the lens surfaces of the first and second lens 51and 52 seems like a flat surface in FIG. 4, while it is not flatsurface. Each of the surfaces of the first and second lenses 51 and 52is a combination surface having four lens portions.

In FIG. 4, the laser beam deflected by the polygon mirror 30 at thehighest point among the four laser beams passes through the highest lensportions of the first and second lenses 51 and 52. The laser beam isreflected by the mirror 71 upwards and then reflected by the mirror 72downwards. The reflected laser beam passes through the third lens 53 aand is converged onto the photoconductive drum 41. In the same manner,the second, third and fourth laser beams from the top pass the second,third fourth lens portions of the first and second lenses 51 and 52, andthey are reflected by the mirrors 73, 75 and 77 to the upside and thenreflected by the mirrors 74, 76 and 78 to the downside, respectively.The reflected second, third and fourth laser beams pass through thethird lenses 53 b, 53 c and 53 d and are converged onto thephotoconductive drums 42, 43 and 44, respectively.

Next, two embodiments of the tandem scanning optical system whosegeneric constructions are shown in FIG. 4 will be described. In thefollowing description, the optical system for the first laser beamdeflected by the polygon mirror 30 at the highest point is taken outfrom the four optical systems. Further, the optical path is developed byomitting the mirrors 71 and 72.

First Embodiment

FIGS. 5 and 6 show a scanning optical system of a first embodiment inthe main scanning direction and in the auxiliary scanning direction,respectively. FIG. 5 shows optical elements from a cylindrical lens 31to the photoconductive drum 41; and FIG. 6 shows optical elements fromthe polygon mirror 30 to the photoconductive drum 41.

The following TABLE 1 shows the numerical construction of the scanningoptical system according to the first embodiment.

Symbol f in the table represents a focal length of the fθ lens in themain scanning direction, W represents the width of the scanning range,ry is a radius of curvature (unit: mm) of a surface in the main scanningdirection, rz denotes a radius of curvature (unit: mm) of a surface inthe auxiliary scanning direction (which will be omitted if a surface isa rotationally-symmetrical surface), d is a distance (unit: mm) betweensurfaces along the optical axis, n is a refractive index of an elementat a design wavelength 780 nm.

Surface numbers 1 and 2 represent the cylindrical lens 31, a number 3represents the reflection surface of the polygon mirror 30, numbers 4and 5 represent the first lens 51 of the fθ lens, numbers 6 and 7represent the second lens 52 of the fθ lens, numbers 8 and 9 representthe third lens 53 a of the fθ lens.

TABLE 1 f = 200.0 mm W = 216 mm Surface Number ry rz d n 1 ∞ 50.00 4.001.51072 2 ∞ — 97.00 3 ∞ — 33.00 4 ∞ — 10.00 1.48617 5 −199.80 — 4.00 6 ∞— 10.00 1.48617 7 −170.00 — 93.00 8 −540.00 30.38 4.00 1.48617 9−1045.00 — 95.10

The surface of number 1 is a cylindrical surface having a power only inthe auxiliary scanning direction, the surfaces of numbers 2 and 3 areflat surfaces, the surfaces of numbers 4, 5, 6, 7 and 9 arerotationally-symmetrical aspherical surfaces, and the surface of number8 is an anamorphic aspherical surface.

A rotationally-symmetrical aspherical surface is defined by distributionof sag amount X(h). The sag X(h) is a distance of the point on theaspherical surface whose distance from the optical axis is h withrespect to the tangential plane at the optical axis. The sags X(h) isexpressed by the following equation (1);

$\begin{matrix}{{X(h)} = {\frac{{Ch}^{2}}{1 + \sqrt{1 - {( {\kappa + 1} )^{2}C^{2}h^{2}}}} + {A_{4}h^{4}} + {A_{6}h^{6}} + {A_{8}h^{8}}}} & (1)\end{matrix}$

Symbol C is a curvature (1/ r) on the optical axis, κ is a constant, A4,A6 and A8 are aspherical surface coefficients of fourth, sixth andeighth orders.

The various constants and coefficients for defining therotationally-symmetrical surfaces are shown in TABLE 2.

TABLE 2 Surface Number κ A₄ A₆ A₈ 4 0.00   3.58 × 10⁻⁶ −5.09 × 10⁻¹⁰0.00 5 0.00   2.84 × 10⁻⁶ −1.33 × 10⁻¹⁰   1.00 × 10⁻¹⁴ 6 0.00   1.03 ×10⁻⁶   1.96 × 10⁻¹¹ 0.00 7 0.00   1.06 × 10⁻⁶   3.00 × 10⁻¹⁰ 0.00 9 0.00−4.47 × 10⁻⁸ −1.53 × 10⁻¹² −1.49 × 10⁻¹⁶

It should be noted that the radii of curvature of the asphericalsurfaces indicated in TABLE 1 are values on the optical axis.

The anamorphic aspherical surface (surface number 8 ) is a surface whoseradius of curvature in the auxiliary scanning direction is determined bythe distance from the optical axis in the main scanning direction and itdoes not have a rotation axis. The anamorphic aspherical surface isdefined by the following two equations (2) and (3).

$\begin{matrix}{{X(Y)} = {\frac{{CY}^{2}}{1 + \sqrt{1 - {( {\kappa + 1} )^{2}C^{2}Y^{2}}}} + {A_{4}Y^{4}} + {A_{6}Y^{6}} + {A_{8}Y^{8}} + {A_{10}Y^{10}}}} & (2) \\{\frac{1}{{rz}(Y)} = {\frac{1}{rz0} + {B_{1}Y} + {B_{2}Y^{2}} + {B_{4}Y^{4}} + {B_{6}Y^{6}}}} & (3)\end{matrix}$

The shape of the anamorphic aspherical surface in the main scanningdirection is defined by the sag X(Y) according to the equation (2). Thesag X(Y) is a distance of the point on the aspherical surface whosedistance from the optical axis is Y in the main scanning direction withrespect to the tangential plane at the optical axis.

A radius of curvature in the auxiliary scanning direction varies inaccordance with the distance Y from the optical axis in the mainscanning direction. The radius of curvature rz(Y) of the surface in theauxiliary scanning direction at the point where the distance from theoptical axis is Y is expressed by the equation (3).

Symbols in the equation (2) are the same as in the equation (1). Thevalues B₁, B₂, B₄ and B₆ are coefficients that define the radius ofcurvature in the auxiliary scanning direction, rz₀ is a radius ofcurvature in the auxiliary scanning direction on the optical axis (equalto rz in TABLE 1). The coefficients that define the surface of number 8are shown in TABLE 3.

TABLE 3 κ 0.00 B₁ −1.89 × 10⁻⁰⁶ A₄    1.08 × 10⁻⁰⁷ B₂ −1.16 × 10⁻⁰⁶ A₆ −1.08 × 10⁻¹¹ B₄   5.36 × 10⁻¹² A₈    3.88 × 10⁻¹⁶ B₆   2.52 × 10⁻¹⁵ A₁₀0.00 — —

FIGS. 7A and 7B are graphs showing the optical performance of thescanning optical system of the first embodiment; FIG. 7A shows alinearity error that is a deviation of the real beam spot with respectto the ideal beam spot in the main scanning direction; and FIG. 7B showsa curvature of field that is a distance from the design image surface tothe beam waist. In the graph of FIG. 7B, a dotted line indicates thevalues in the main-scanning direction and a solid line indicates thevalues in the auxiliary scanning direction.

Second Embodiment

FIGS. 8 and 9 show a scanning optical system of a second embodiment inthe main scanning direction and in the auxiliary scanning direction,respectively. The following TABLE 4 shows the numerical construction ofthe scanning optical system according to the second embodiment. Therelationship between the surface numbers and the optical elements areidentical to the first embodiment.

TABLE 4 f = 200.0 mm W = 216 mm Surface Number Ry rz d n 1 ∞ 50.00 4.001.51072 2 ∞ — 97.00 3 ∞ — 46.50 4 −75.00 1000.00 5.00 1.48617 5 −69.10−400.70 2.00 6 ∞ — 10.00 1.51072 7 −115.80 ∞ 106.50 8 −722.70 29.71 4.001.48617 9 −1750.80 — 90.00

The surface of number 1 is a cylindrical surface having a power only inthe auxiliary scanning direction, the surfaces of number 2, 3 and 6 areflat surfaces, the surfaces of numbers 4 and 5 are toric asphericalsurfaces, the surface of number 7 is a cylindrical surface having apower only in the main scanning direction, the surface of number 8 is ananamorphic aspherical surface and the surface of number 9 is arotationally-symmetrical aspherical surface.

The toric aspherical surface is defined by the shape in scanningdirection that is represented by the equation (2) and the radius ofcurvature in the auxiliary scanning direction rz. The toric asphericalsurface is defined as a locus of the aspherical curve line defined bythe equation (2) when the aspherical curve line rotates about the axisextending in the main scanning direction that crosses the optical axisat the point whose distance from the surface along the optical axisequals to rz.

The various constants and coefficients for defining the toric asphericalsurfaces and the rotationally-symmetrical surface are shown in TABLE 5.The various constants and coefficients for defining the anamorphicaspherical surface are shown in TABLE 6.

TABLE 5 Surface Number κ A₄ A₆ A₈ 4 0.00   2.93 × 10⁻⁶ 2.35 × 10⁻¹⁰ 0.005 0.00   2.56 × 10⁻⁶ 3.83 × 10⁻¹⁰ 0.00 9 0.00 −3.82 × 10⁻⁸ 3.35 × 10⁻¹²−3.09 × 10⁻¹⁶

TABLE 6 κ 0.00 B₁ −1.18 × 10⁻⁰⁶ A₄    5.39 × 10⁻⁰⁸ B₂ −9.25 × 10⁻⁰⁷ A₆ −3.29 × 10⁻¹² B₄   2.30 × 10⁻¹¹ A₈    6.43 × 10⁻¹⁸ B₆ 0.00 A₁₀ 0.00 — —

FIGS. 10A and 10B are graphs showing the optical performance of thescanning optical system of the second embodiment; FIG. 10A shows thelinearity error; and FIG. 10B shows the curvature of field.

When the scanning optical systems of the first and second embodimentsare applied to the tandem scanning optical system of FIG. 4, each of thefirst and second lenses 51 and 52 is formed as the complex lens havingfour lens portions, each of which is designed according to the data ofthe embodiments, stacked in the auxiliary scanning direction, and thethird lens 53 a designed according to the data of the embodiments isalso employed as the other third lenses 53 b to 53 d.

Further, the complex lens is molded by the injection molding of theresin in the embodiment, while the method of the invention can beapplied to another molding method employing the molding dies, such as amethod to manufacture a glass molding lens or a hybrid lens having aresin layer on a glass lens.

As described above, since the lens surfaces of the complex lens at theincident side are formed by the single-piece mirror surface core and thelens surfaces at the exit side are formed by the other single-piecemirror surface core, the relative positional error among the lenssurfaces at the incident side and that at the exit side can be reduced.

Further, when the mirror surface portions have concave sectional shapesin the auxiliary scanning direction, the boundary portions can besharply processed by the cutting tool. Therefore, the mirror surfaceportions can be processed without the margins at the boundary portions,which avoids upsizing of the lens surfaces in the auxiliary scanningdirection more than necessary.

The present disclosure relates to subject matter contained in JapanesePatent Application No. 2000-358852 filed on Nov. 27, 2000, which isexpressly incorporated herein by reference in its entirety.

What is claimed is:
 1. A complex lens for a tandem scanning opticalsystem that converges a plurality of light beams, which are modulatedindependently and deflected by a single deflector, onto a surface to bescanned, to scan a plurality of lines on the surface at the same time,said complex lens comprising: a plurality of stacked lens portions thatare molded as a single-piece element, wherein a plurality of lenssurfaces of said lens portions at an incident side are formed by a firstsingle-piece mirror surface core and a plurality of lens surfaces ofsaid lens portions at an exit side are formed by a second single-piecemirror surface core during the molding, each of the first and secondsingle-piece mirror surface cores having a plurality of mirror surfaceportions, the plurality of mirror surface portions of the firstsingle-piece mirror surface core respectively forming a plurality oflens surfaces at the incident side, the plurality of mirror surfaceportions of the second single-piece mirror surface core respectivelyforming a plurality of lens surfaces at the exit side, wherein theplurality of lens surfaces on the incident side and on the exit side areconfigured to be spaced in a direction transverse to a scan direction.2. The complex lens according to claim 1, wherein each of said lensportions has a convex sectional shape in a direction perpendicular tothe direction in which a plurality of light beams scan.
 3. The complexlens according to claim 1, wherein said lens surfaces of at least one ofthe incident and exit sides are formed as rotationally-symmetricalconvex surfaces with respect to respective optical axes.
 4. The complexlens according to claim 1, said stacked lens portions being integrallymolded.